Plane rendering order depends on camera position/angle
That is caused by floating point errors, depending on the distance to the camera. When the values get too high, the precision is not enough to properly sort the objects, especially when they are only 0.1 units apart. You can try to remedy this by adjusting the camera far clipping plane value in the camera properties or increasing the distance between the two planes.



EDIT: just now saw the screenshots - that does look like the far clipping plane. Decrease its value and you should be fine.